Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Quantum-geometric spin and charge Josephson diode effects

Niklas L. Schulz*, Danilo Nikolić†, and Matthias Eschrig‡

  • *Contact author: niklas.schulz@uni-greifswald.de
  • †Contact author: danilo.nikolic@uni-greifswald.de
  • ‡Contact author: matthias.eschrig@uni-greifswald.de

Phys. Rev. B 112, 104514 – Published 26 September, 2025

DOI: https://doi.org/10.1103/nb38-v1jq

Abstract

We present a general mechanism for large charge and spin Josephson diode effects in strongly spin-polarized superconductor-ferromagnet hybrid structures with a noncoplanar spin texture, formulated in terms of quantum-geometric phases. We present necessary conditions for this effect to occur, and show numerical results for disordered materials relevant to applications. We calculate Josephson diode efficiencies for both charge and spin diodes and show that a spin-diode efficiency of 100% can be reached. Finally, we present a SQUID device that can switch between nearly pure spin-up and spin-down equal-spin supercurrents across the ferromagnet by reversing the flux. These findings establish functionalities that are absent in coplanar spin textures.

View figure in article

Physics Subject Headings (PhySH)

Corrections

31 August, 2026

Correction: A typographical error in Eq. (1) has been fixed.

See Also

Article Text

References (54)

  1. M. Eschrig, Spin-polarized supercurrents for spintronics: A review of current progress, Rep. Prog. Phys. 78, 104501 (2015).
  2. J. Linder and J. W. A. Robinson, Superconducting spin-tronics, Nat. Phys. 11, 307 (2015).
  3. G. Yang, C. Ciccarelli, and J. W. A. Robinson, Boosting spintronics with superconductivity, APL Mater. 9, 050703 (2021).
  4. R. Cai, I. Žutić, and W. Han, Superconductor/ferromagnet heterostructures: A platform for superconducting spintronics and quantum computation, Adv. Quantum Technol. 6, 2200080 (2023).
  5. R. S. Keizer, S. T. B. Goennenwein, T. M. Klapwijk, G. Miao, G. Xiao, and A. Gupta, A spin triplet supercurrent through the half-metallic ferromagnet CrO2, Nature (London) 439, 825 (2006).
  6. T. S. Khaire, M. A. Khasawneh, W. P. Pratt, and N. O. Birge, Observation of spin-triplet superconductivity in Co-based Josephson junctions, Phys. Rev. Lett. 104, 137002 (2010).
  7. M. S. Anwar, F. Czeschka, M. Hesselberth, M. Porcu, and J. Aarts, Long-range supercurrents through half-metallic ferromagnetic CrO2, Phys. Rev. B 82, 100501(R) (2010).
  8. J. W. A. Robinson, J. D. S. Witt, and M. G. Blamire, Controlled injection of spin-triplet supercurrents into a strong ferromagnet, Science 329, 59 (2010).
  9. N. O. Birge, Spin-triplet supercurrents in Josephson junctions containing strong ferromagnetic materials, Philos. Trans. R. Soc. A 376, 20150150 (2018).
  10. J. A. Glick, A. B. Gougam, B. M. Niedzielski, E. C. Gingrich, R. Loloee, W. P. Pratt Jr., and N. O. Birge, Phase control in a spin-triplet SQUID, Sci. Adv. 4, eaat9457 (2018).
  11. R. Caruso, D. Massarotti, G. Campagnano, A. Pal, H. G. Ahmad, P. Lucignano, M. Eschrig, M. G. Blamire, and F. Tafuri, Tuning of magnetic activity in spin-filter Josephson junctions towards spin-triplet transport, Phys. Rev. Lett. 122, 047002 (2019).
  12. V. Aguilar, D. Korucu, J. A. Glick, R. Loloee, W. P. Pratt, Jr., and N. O. Birge, Spin-polarized triplet supercurrent in Josephson junctions with perpendicular ferromagnetic layers, Phys. Rev. B 102, 024518 (2020).
  13. N. O. Birge and N. Satchell, Ferromagnetic materials for Josephson π junctions, APL Mater. 12, 041105 (2024).
  14. R. Grein, M. Eschrig, G. Metalidis, and G. Schön, Spin-dependent Cooper pair phase and pure spin supercurrents in strongly polarized ferromagnets, Phys. Rev. Lett. 102, 227005 (2009).
  15. M. Eschrig, Spin-polarized supercurrents for spintronics, Phys. Today 64, 43 (2011).
  16. L. Šmejkal, J. Sinova, and T. Jungwirth, Emerging research landscape of altermagnetism, Phys. Rev. X 12, 040501 (2022).
  17. B. A. Bernevig, T. L. Hughes, and S.-C. Zhang, Quantum spin Hall effect and topological phase transition in HgTe quantum wells, Science 314, 1757 (2006).
  18. D. Hsieh, D. Qian, L. Wray, Y. Xia, Y. S. Hor, R. J. Cava, and M. Z. Hasan, A topological Dirac insulator in a quantum spin Hall phase, Nature (London) 452, 970 (2008).
  19. Y. Ando, Topological insulator materials, J. Phys. Soc. Jpn. 82, 102001 (2013).
  20. U. K. Rößler, A. N. Bogdanov, and C. Pfleiderer, Spontaneous skyrmion ground states in magnetic metals, Nature (London) 442, 797 (2006).
  21. X. Z. Yu, Y. Onose, N. Kanazawa, J. H. Park, J. H. Han, Y. Matsui, N. Nagaosa, and Y. Tokura, Real-space observation of a two-dimensional skyrmion crystal, Nature (London) 465, 901 (2010).
  22. A. Fert, N. Reyren, and V. Cros, Magnetic skyrmions: Advances in physics and potential applications, Nat. Rev. Mater. 2, 17031 (2017).
  23. M. Eschrig, Phase-sensitive interface and proximity effects in superconducting spintronics, in Spintronics Handbook, Second Edition: Spin Transport and Magnetism: Volume One: Metallic Spintronics, edited by E. Tsymbal and I. Žutić (CRC Press, Boca Raton, FL, 2019), pp. 635–682.
  24. J. Hu, C. Wu, and X. Dai, Proposed design of a Josephson diode, Phys. Rev. Lett. 99, 067004 (2007).
  25. A. A. Reynoso, G. Usaj, C. A. Balseiro, D. Feinberg, and M. Avignon, Anomalous Josephson current in junctions with spin polarizing quantum point contacts, Phys. Rev. Lett. 101, 107001 (2008).
  26. I. Margaris, V. Paltoglou, and N. Flytzanis, Zero phase difference supercurrent in ferromagnetic Josephson junctions, J. Phys.: Condens. Matter 22, 445701 (2010).
  27. S. Ilić and F. S. Bergeret, Theory of the supercurrent diode effect in Rashba superconductors with arbitrary disorder, Phys. Rev. Lett. 128, 177001 (2022).
  28. R. S. Souto, M. Leijnse, and C. Schrade, Josephson diode effect in supercurrent interferometers, Phys. Rev. Lett. 129, 267702 (2022).
  29. M. Davydova, S. Prembabu, and L. Fu, Universal Josephson diode effect, Sci. Adv. 8, eabo0309 (2022).
  30. J. J. He, Y. Tanaka, and N. Nagaosa, A phenomenological theory of superconductor diodes, New J. Phys. 24, 053014 (2022).
  31. T. Karabassov, I. V. Bobkova, A. A. Golubov, and A. S. Vasenko, Hybrid helical state and superconducting diode effect in superconductor/ferromagnet/topological insulator heterostructures, Phys. Rev. B 106, 224509 (2022).
  32. M. Nadeem, M. S. Fuhrer, and X. Wang, The superconducting diode effect, Nat. Rev. Phys. 5, 558 (2023).
  33. J. S. Meyer and M. Houzet, Josephson diode effect in a ballistic single-channel nanowire, Appl. Phys. Lett. 125, 022603 (2024).
  34. C. Sun, J. B. Tjernshaugen, and J. Linder, Voltage-tunable spin supercurrent nonreciprocity reaching 100% efficiency, Phys. Rev. B 112, 064504 (2025).
  35. F. Ando, Y. Miyasaka, T. Li, J. Ishizuka, T. Arakawa, Y. Shiota, T. Moriyama, Y. Yanase, and T. Ono, Observation of superconducting diode effect, Nature (London) 584, 373 (2020).
  36. C. Baumgartner, L. Fuchs, A. Costa, S. Reinhardt, S. Gronin, G. C. Gardner, T. Lindemann, M. J. Manfra, P. E. Faria Jr., D. Kochan, J. Fabian, N. Paradiso, and C. Strunk, Supercurrent rectification and magnetochiral effects in symmetric Josephson junctions, Nat. Nanotechnol. 17, 39 (2022).
  37. E. Strambini, M. Spies, N. Ligato, S. Ilić, M. Rouco, C. Gonzalez-Orellana, M. Ilyn, C. Rogero, F. S. Bergeret, J. S. Moodera, P. Virtanen, T. T. Heikkilä, and F. Giazotto, Superconducting spintronic tunnel diode, Nat. Commun. 13, 2431 (2022).
  38. Y. Hou, F. Nichele, H. Chi, A. Lodesani, Y. Wu, M. F. Ritter, D. Z. Haxell, M. Davydova, S. Ilić, O. Glezakou-Elbert, A. Varambally, F. S. Bergeret, A. Kamra, L. Fu, P. A. Lee, and J. S. Moodera, Ubiquitous superconducting diode effect in superconductor thin films, Phys. Rev. Lett. 131, 027001 (2023).
  39. M. Trahms, L. Melischek, J. F. Steiner, B. Mahendru, I. Tamir, N. Bogdanoff, O. Peters, G. Reecht, C. B. Winkelmann, F. von Oppen, and K. J. Franke, Diode effect in Josephson junctions with a single magnetic atom, Nature (London) 615, 628 (2023).
  40. W. Belzig, F. K. Wilhelm, C. Bruder, G. Schön, and A. D. Zaikin, Quasiclassical Green's function approach to mesoscopic superconductivity, Superlattices Microstruct. 25, 1251 (1999).
  41. K. D. Usadel, Generalized diffusion equation for super-conducting alloys, Phys. Rev. Lett. 25, 507 (1970).
  42. N. L. Schulz, D. Nikolić, and M. Eschrig, following paper, Theory of quantum-geometric charge and spin Josephson diode effects in strongly spin-polarized hybrid structures with noncoplanar spin textures, Phys. Rev. B 112, 104515 (2025).
  43. M. Eschrig, A. Cottet, W. Belzig, and J. Linder, General boundary conditions for quasiclassical theory of superconductivity in the diffusive limit: Application to strongly spin-polarized systems, New J. Phys. 17, 083037 (2015).
  44. R. Grein, T. Löfwander, G. Metalidis, and M. Eschrig, Theory of superconductor-ferromagnet point-contact spectra: The case of strong spin polarization, Phys. Rev. B 81, 094508 (2010).
  45. V. B. Geshkenbein and A. I. Larkin, The Josephson effect in superconductors with heavy fermions, Pis'ma Zh. Eksp. Teor. Fiz. 43, 306 (1986) [JETP Lett. 43, 395 (1986)].
  46. M. Sigrist, Time-reversal symmetry breaking states in high-temperature superconductors, Prog. Theor. Phys. 99, 899 (1998).
  47. V. Braude and Yu. V. Nazarov, Fully developed triplet proximity effect, Phys. Rev. Lett. 98, 077003 (2007).
  48. Y. Asano, Y. Tanaka, and A. A. Golubov, Josephson effect due to odd-frequency pairs in diffusive half metals, Phys. Rev. Lett. 98, 107002 (2007).
  49. M. Eschrig and T. Löfwander, Triplet supercurrents in clean and disordered half-metallic ferromagnets, Nat. Phys. 4, 138 (2008).
  50. A. Buzdin, Direct coupling between magnetism and superconducting current in the Josephson φ0 junction, Phys. Rev. Lett. 101, 107005 (2008).
  51. B. Béri, J. N. Kupferschmidt, C. W. J. Beenakker, and P. W. Brouwer, Quantum limit of the triplet proximity effect in half-metal–superconductor junctions, Phys. Rev. B 79, 024517 (2009).
  52. J. S. Moodera, T. S. Santos, and T. Nagahama, The phenomena of spin-filter tunnelling, J. Phys.: Condens. Matter 19, 165202 (2007).
  53. V. Risinggård and J. Linder, Direct and inverse superspin Hall effect in two-dimensional systems: Electrical detection of spin supercurrents, Phys. Rev. B 99, 174505 (2019).
  54. N. L. Schulz, D. Nikolić, and M. Eschrig, Data for “Quantum-geometric spin- and charge Josephson diode effects”, Zenodo (2025), doi:10.5281/zenodo.16925237.

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation